Symbols
The invariant may be computed for a specific symbol φ taking values ±1 in the group C2.
In the context of quadratic forms over a local field, the Hasse invariant may be defined using the Hilbert symbol, the unique symbol taking values in C2. The invariants of a quadratic forms over a local field are precisely the dimension, discriminant and Hasse invariant.
For quadratic forms over a number field, there is a Hasse invariant ±1 for every finite place. The invariants of a form over a number field are precisely the dimension, discriminant, all local Hasse invariants and the signatures coming from real embeddings.
Read more about this topic: Hasse Invariant Of A Quadratic Form
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